src/math/Polynomial.hpp

/*
 * Copyright (C) 2000-2004  Object Oriented Parallel Simulation Engine (OOPSE) project
 * 
 * Contact: oopse@oopse.org
 * 
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License
 * as published by the Free Software Foundation; either version 2.1
 * of the License, or (at your option) any later version.
 * All we ask is that proper credit is given for our work, which includes
 * - but is not limited to - adding the above copyright notice to the beginning
 * of your source code files, and to any copyright notice that you may distribute
 * with programs based on this work.
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
 *
 */

/**
 * @file Polynomial.hpp
 * @author    teng lin
 * @date  11/16/2004
 * @version 1.0
 */ 

#ifndef MATH_POLYNOMIAL_HPP
#define MATH_POLYNOMIAL_HPP

#include <list>
#include <utility>
#include <map>

namespace oopse {

template<typename ElemType> pow(ElemType x, int N) {
    ElemType result(1);

    for (int i = 0; i < N; ++i) {
        result *= x;
    }

    return result;
}

/**
 * @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
 * A generic Polynomial class
 */
template<typename ElemType>
class Polynomial {

    public:
        
        typedef int ExponentType;
        typedef ElemType CoefficientType;
        typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
        typedef PolynomialPairMap::iterator PolynomialIterator;

        /** 
         * Calculates the value of this Polynomial evaluated at the given x value.
         * @return The value of this Polynomial evaluates at the given x value
         * @param x the value of the independent variable for this Polynomial function
         */
        ElemType evaluate(const ElemType& x) {
            ElemType result;
            double exponent;
            double coefficient;
            
            for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
                exponent = i->first;
                coefficient = i->second;
                result  += pow(x, exponent) * coefficient;
            }

            return result;
        }

        /**
         * Returns the first derivative of this polynomial.
         * @return the first derivative of this polynomial
         * @param x
         */
        ElemType evaluateDerivative(const ElemType& x) {
            ElemType result;
            double exponent;
            double coefficient;
            
            for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
                exponent = i->first;
                coefficient = i->second;
                result  += pow(x, exponent - 1) * coefficient * exponent;
            }

            return result;
        }

        /**
         * Set the coefficent of the specified exponent, if the coefficient is already there, it
         * will be overwritten.
         * @param exponent exponent of a term in this Polynomial 
         * @param coefficient multiplier of a term in this Polynomial 
         */
        
        void setCoefficient(int exponent, const ElemType& coefficient) {
            polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient));
        }

        /**
         * Set the coefficent of the specified exponent. If the coefficient is already there,  just add the
         * new coefficient to the old one, otherwise,  just call setCoefficent
         * @param exponent exponent of a term in this Polynomial 
         * @param coefficient multiplier of a term in this Polynomial 
         */
        
        void addCoefficient(int exponent, const ElemType& coefficient) {
            PolynomialIterator i = find(exponent);

            if (i != end()) {
                i->second += coefficient;
            } else {
                setCoefficient(exponent, coefficient);
            }
        }


        /**
         * Returns the coefficient associated with the given power for this Polynomial.
         * @return the coefficient associated with the given power for this Polynomial
         * @exponent exponent of any term in this Polynomial
         */
        ElemType getCoefficient(ExponentType exponent) {
            PolynomialIterator i = find(exponent);

            if (i != end()) {
                return i->second;
            } else {
                return ElemType(0);
            }
        }

        PolynomialIterator begin() {
            return polyPairMap_.begin();
        }
        
        PolynomialIterator end() {
            return polyPairMap_.end();
        }

        PolynomialIterator find(ExponentType exponent) {
            return polyPairMap_.find();
        }

        size_t size() {
            return polyPairMap_.size();
        }
        
    private:
        
        PolynomialPairMap polyPairMap_;
};


/**
 * Generates and returns the product of two given Polynomials.
 * @return A Polynomial containing the product of the two given Polynomial parameters
 */
template<typename ElemType>
Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
    typename Polynomial<ElemType>::PolynomialIterator i;
    typename Polynomial<ElemType>::PolynomialIterator j;
    typename Polynomial<ElemType>::PolynomialIterator k;
    Polynomial<ElemType> p;
    int exponent;
    int coefficient;
    
    for (i = p1.begin(); i !=p1.end(); ++i) {
        for (j = p1.begin(); j !=p1.end(); ++j) {
            exponent = i->first + j->first;            
            coefficient = i->second * j->second;
            k = p->find(exponent);

            if (k != p.end()) {
                p[exponent] = coefficient;
            } else {
                k->second += coefficient;
            }
        }
    }
}

/**
 * Generates and returns the sum of two given Polynomials.
 * @param p1 the first polynomial
 * @param p2 the second polynomial
 */
template<typename ElemType>
Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
    Polynomial<ElemType> p(p1);

    typename Polynomial<ElemType>::PolynomialIterator i;
    typename Polynomial<ElemType>::PolynomialIterator j;

    for (i =  p2.begin(); i  != p2.end(); ++i) {
        j = p.find(i->first);
        if (j == p.end()) {
            p[j] = i->second;
        } else {
            j->second += i->second;
        }
    }

    return p;

}

/**
 * Generates and returns the difference of two given Polynomials. 
 * @return
 * @param p1 the first polynomial
 * @param p2 the second polynomial
 */
template<typename ElemType>
Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
    Polynomial<ElemType> p(p1);

    typename Polynomial<ElemType>::PolynomialIterator i;
    typename Polynomial<ElemType>::PolynomialIterator j;

    for (i =  p2.begin(); i  != p2.end(); ++i) {
        j = p.find(i->first);
        if (j == p.end()) {
            p[j] = -i->second;
        } else {
            j->second -= i->second;
        }
    }

    return p;

}

/**
 * Tests if two polynomial have the same exponents
 * @return true if these all of the exponents in these Polynomial are identical
 * @param p1 the first polynomial
 * @param p2 the second polynomial
 * @note this function does not compare the coefficient
 */
template<typename ElemType>
bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {

    typename Polynomial<ElemType>::PolynomialIterator i;
    typename Polynomial<ElemType>::PolynomialIterator j;

    if (p1.size() !== p2.size() ) {
        return false;
    }
    
    for (i =  p1.begin(), j = p2.begin(); i  != p1.end() && j != p2.end(); ++i, ++j) {
        if (i->first != j->first) {
            return false;
        }
    }

    return true;
}

typedef Polynomial<double> DoublePolynomial;

} //end namespace oopse
#endif //MATH_POLYNOMIAL_HPP
Revision:	1786
Committed:	Fri Nov 26 02:13:56 2004 UTC (19 years, 9 months ago) by tim
File size:	8385 byte(s)
Log Message:	rename some files
#	User	Rev	Content
1	tim	1744	/*
2			* Copyright (C) 2000-2004 Object Oriented Parallel Simulation Engine (OOPSE) project
3			*
4			* Contact: oopse@oopse.org
5			*
6			* This program is free software; you can redistribute it and/or
7			* modify it under the terms of the GNU Lesser General Public License
8			* as published by the Free Software Foundation; either version 2.1
9			* of the License, or (at your option) any later version.
10			* All we ask is that proper credit is given for our work, which includes
11			* - but is not limited to - adding the above copyright notice to the beginning
12			* of your source code files, and to any copyright notice that you may distribute
13			* with programs based on this work.
14			*
15			* This program is distributed in the hope that it will be useful,
16			* but WITHOUT ANY WARRANTY; without even the implied warranty of
17			* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18			* GNU Lesser General Public License for more details.
19			*
20			* You should have received a copy of the GNU Lesser General Public License
21			* along with this program; if not, write to the Free Software
22			* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
23			*
24			*/
25
26			/**
27			* @file Polynomial.hpp
28	tim	1746	* @author teng lin
29			* @date 11/16/2004
30	tim	1744	* @version 1.0
31			*/
32
33			#ifndef MATH_POLYNOMIAL_HPP
34			#define MATH_POLYNOMIAL_HPP
35
36			#include <list>
37			#include <utility>
38	tim	1786	#include <map>
39	tim	1744
40			namespace oopse {
41
42	tim	1746	template<typename ElemType> pow(ElemType x, int N) {
43	tim	1744	ElemType result(1);
44
45			for (int i = 0; i < N; ++i) {
46			result *= x;
47			}
48
49			return result;
50			}
51
52	tim	1746	/**
53			* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
54			* A generic Polynomial class
55			*/
56	tim	1744	template<typename ElemType>
57			class Polynomial {
58
59			public:
60
61			typedef int ExponentType;
62	tim	1746	typedef ElemType CoefficientType;
63			typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
64	tim	1744	typedef PolynomialPairMap::iterator PolynomialIterator;
65
66			/**
67	tim	1746	* Calculates the value of this Polynomial evaluated at the given x value.
68			* @return The value of this Polynomial evaluates at the given x value
69			* @param x the value of the independent variable for this Polynomial function
70	tim	1744	*/
71			ElemType evaluate(const ElemType& x) {
72			ElemType result;
73			double exponent;
74	tim	1746	double coefficient;
75	tim	1744
76			for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
77			exponent = i->first;
78	tim	1746	coefficient = i->second;
79			result += pow(x, exponent) * coefficient;
80	tim	1744	}
81
82			return result;
83			}
84
85	tim	1746	/**
86			* Returns the first derivative of this polynomial.
87			* @return the first derivative of this polynomial
88			* @param x
89			*/
90			ElemType evaluateDerivative(const ElemType& x) {
91	tim	1744	ElemType result;
92			double exponent;
93	tim	1746	double coefficient;
94	tim	1744
95			for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
96			exponent = i->first;
97	tim	1746	coefficient = i->second;
98			result += pow(x, exponent - 1) * coefficient * exponent;
99	tim	1744	}
100
101			return result;
102			}
103
104	tim	1746	/**
105	tim	1747	* Set the coefficent of the specified exponent, if the coefficient is already there, it
106			* will be overwritten.
107	tim	1746	* @param exponent exponent of a term in this Polynomial
108			* @param coefficient multiplier of a term in this Polynomial
109			*/
110
111			void setCoefficient(int exponent, const ElemType& coefficient) {
112			polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient));
113	tim	1744	}
114
115	tim	1746	/**
116	tim	1747	* Set the coefficent of the specified exponent. If the coefficient is already there, just add the
117			* new coefficient to the old one, otherwise, just call setCoefficent
118			* @param exponent exponent of a term in this Polynomial
119			* @param coefficient multiplier of a term in this Polynomial
120			*/
121
122			void addCoefficient(int exponent, const ElemType& coefficient) {
123			PolynomialIterator i = find(exponent);
124
125			if (i != end()) {
126			i->second += coefficient;
127			} else {
128			setCoefficient(exponent, coefficient);
129			}
130			}
131
132
133			/**
134	tim	1746	* Returns the coefficient associated with the given power for this Polynomial.
135			* @return the coefficient associated with the given power for this Polynomial
136			* @exponent exponent of any term in this Polynomial
137			*/
138			ElemType getCoefficient(ExponentType exponent) {
139			PolynomialIterator i = find(exponent);
140	tim	1744
141	tim	1746	if (i != end()) {
142			return i->second;
143			} else {
144			return ElemType(0);
145			}
146	tim	1744	}
147
148			PolynomialIterator begin() {
149			return polyPairMap_.begin();
150			}
151
152			PolynomialIterator end() {
153			return polyPairMap_.end();
154			}
155
156			PolynomialIterator find(ExponentType exponent) {
157			return polyPairMap_.find();
158			}
159	tim	1746
160			size_t size() {
161			return polyPairMap_.size();
162			}
163
164	tim	1744	private:
165
166			PolynomialPairMap polyPairMap_;
167			};
168
169	tim	1746
170			/**
171			* Generates and returns the product of two given Polynomials.
172			* @return A Polynomial containing the product of the two given Polynomial parameters
173			*/
174			template<typename ElemType>
175			Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
176			typename Polynomial<ElemType>::PolynomialIterator i;
177			typename Polynomial<ElemType>::PolynomialIterator j;
178			typename Polynomial<ElemType>::PolynomialIterator k;
179			Polynomial<ElemType> p;
180			int exponent;
181			int coefficient;
182
183			for (i = p1.begin(); i !=p1.end(); ++i) {
184	tim	1747	for (j = p1.begin(); j !=p1.end(); ++j) {
185	tim	1746	exponent = i->first + j->first;
186			coefficient = i->second * j->second;
187			k = p->find(exponent);
188
189			if (k != p.end()) {
190			p[exponent] = coefficient;
191			} else {
192			k->second += coefficient;
193			}
194			}
195			}
196			}
197
198			/**
199			* Generates and returns the sum of two given Polynomials.
200			* @param p1 the first polynomial
201			* @param p2 the second polynomial
202			*/
203			template<typename ElemType>
204			Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
205			Polynomial<ElemType> p(p1);
206
207			typename Polynomial<ElemType>::PolynomialIterator i;
208			typename Polynomial<ElemType>::PolynomialIterator j;
209
210			for (i = p2.begin(); i != p2.end(); ++i) {
211			j = p.find(i->first);
212			if (j == p.end()) {
213			p[j] = i->second;
214			} else {
215			j->second += i->second;
216			}
217			}
218
219			return p;
220
221			}
222
223			/**
224			* Generates and returns the difference of two given Polynomials.
225			* @return
226			* @param p1 the first polynomial
227			* @param p2 the second polynomial
228			*/
229			template<typename ElemType>
230			Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
231			Polynomial<ElemType> p(p1);
232
233			typename Polynomial<ElemType>::PolynomialIterator i;
234			typename Polynomial<ElemType>::PolynomialIterator j;
235
236			for (i = p2.begin(); i != p2.end(); ++i) {
237			j = p.find(i->first);
238			if (j == p.end()) {
239			p[j] = -i->second;
240			} else {
241			j->second -= i->second;
242			}
243			}
244
245			return p;
246
247			}
248
249			/**
250			* Tests if two polynomial have the same exponents
251			* @return true if these all of the exponents in these Polynomial are identical
252			* @param p1 the first polynomial
253			* @param p2 the second polynomial
254			* @note this function does not compare the coefficient
255			*/
256			template<typename ElemType>
257			bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
258
259			typename Polynomial<ElemType>::PolynomialIterator i;
260			typename Polynomial<ElemType>::PolynomialIterator j;
261
262			if (p1.size() !== p2.size() ) {
263			return false;
264			}
265
266			for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
267			if (i->first != j->first) {
268			return false;
269			}
270			}
271
272			return true;
273			}
274
275			typedef Polynomial<double> DoublePolynomial;
276
277	tim	1744	} //end namespace oopse
278			#endif //MATH_POLYNOMIAL_HPP